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Derivative as a Rate Measurer Maths - Derivative as a Rate Measurer

Maharashtra Board - STD 12 - Maths (MSBSHSE - Semi English Medium). 78 questions in this chapter.

Question types

Derivative as a Rate Measurer question types

78 questions across 4 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

78
Questions
4
Question groups
5
Question types
Sample Questions

Derivative as a Rate Measurer questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1MCQ1 Mark
If $s = t^3- 4t^2+ 5$ describes the motion of a particle, then its velocity when the acceleration vanishes, is:
  • A
    $\frac{16}{2}\ \text{unit}/\text{sec}.$
  • B
    $\frac{\text{-32}}{3}\ \text{unit}/\text{sec}.$
  • C
    $\frac{4}{3}\ \text{unit}/\text{sec}.$
  • ✓
    $-\frac{16}{3}\ \text{unit}/\text{sec}.$

Answer: D.

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Q 2MCQ1 Mark
A man of height $6ft$ walks at a uniform speed of $9ft/\sec.$ from a lamp fixed at $15ft$ height. The length of his shadow is increasing at the rate of:
  • A
    $15\text{ft}/\text{sec}.$
  • B
    $9\text{ft}/\text{sec}.$
  • ✓
    $6\text{ft}/\text{sec}.$
  • D
    None of these.

Answer: C.

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Q 3MCQ1 Mark
The radius of the base of a cone is increasing at the rate of $3\ \text{cm/minute}$ and the altitude is decreasing at the rate of $4\ \text{cm/minute.}$ The rate of change of lateral surface when the radius $= 7\ cm$ and altitude $24\ cm$ is:
  • ✓
    $54\pi \text{cm}^{2}/\text{min}$
  • B
    $7\pi\text{cm}^{2}/\text{min}$
  • C
    $27\text{cm}^{2}/\text{min}$
  • D
    $\text{none of these }$

Answer: A.

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Q 4MCQ1 Mark
Side of an equilateral triangle expands at the rate of $2\text{cm}/ \text{sec}.$ The rate of increase of its area when each side is $10\ cm$ is:
  • A
    $10\sqrt{2}\text{cm}^2/\sec.$
  • ✓
    $10\sqrt{3}\text{cm}^2/\sec.$
  • C
    $10\text{cm}^2/\sec.$
  • D
    $5\text{cm}^2/\sec.$

Answer: B.

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Q 5MCQ1 Mark
The equation of motion of a particle is $\text{s} = \text{2t}^2 + \sin\text{2t,}$ where s is in metres and t is in seconds. The velocity of the particle when its acceleration is $2m/\sec^2$, is:
  • A
    $\pi+\sqrt{3}\text{m}/\text{sec}.$
  • ✓
    $\frac{\pi}{3}+\sqrt{3}\text{m}/\text{sec}.$
  • C
    $\frac{2\pi}{3}+\sqrt{3}\text{m}/\text{sec}.$
  • D
    $\frac{\pi}{3}+\frac{1}{\sqrt{3}}\text{m}/\text{sec}.$

Answer: B.

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Q 16Solve the Following Question.(5 Marks)5 Marks
Water is running into an inverted cone at the rate of $\pi$ cubic metres per minute. The height of the cone is 10 metres, and the radius of its base is 5m. How fast the water level is rising when the water stands 7.5m below the base.
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Q 19Solve the Following Question.(5 Marks)5 Marks
The top of a ladder $6$ metres long is resting against a vertical wall on a level pavement, when the ladder begins to slide outwards. At the moment when the foot of the ladder is $4$ metres from the wall, it is sliding away from the wall at the rate of 0.5m/ sec. How fast is the top-sliding downwards at this instance?
How far is the foot from the wall when it and the top are moving at the same rate?
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